אִ֣ם הַכֹּהֵ֧ן הַמָּשִׁ֛יחַ יֶֽחֱטָ֖א לְאַשְׁמַ֣ת הָעָ֑ם וְהִקְרִ֡יב עַ֣ל חַטָּאתוֹ֩ אֲשֶׁ֨ר חָטָ֜א פַּ֣ר בֶּן־בָּקָ֥ר תָּמִ֛ים לַֽיהוָ֖ה לְחַטָּֽאת׃
If the anointed priest shall sin so as to bring guilt on the people, then let him offer for his sin, which he hath sinned, a young bullock without blemish unto the LORD for a sin-offering.
Initially I thought that these were special priests, but eventually all priests were anointed during the era of the Torah as this week's portion tells us (Vayikra 7:36):
אֲשֶׁר֩ צִוָּ֨ה יְהוָ֜ה לָתֵ֣ת לָהֶ֗ם בְּיוֹם֙ מָשְׁח֣וֹ אֹתָ֔ם מֵאֵ֖ת בְּנֵ֣י יִשְׂרָאֵ֑ל חֻקַּ֥ת עוֹלָ֖ם לְדֹֽרֹתָֽם׃
Which Hashem commanded to be given them of the children of Israel, in the day that they were anointed. It is a due for ever throughout their generations.
Even Wikipedia discusses the issue. So if all priests were anointed, why was it relevant to add this word last week? If only the high priest was anointed, how can the second verse be explained?